A laser that is powerful enough to hurt a human target (especially a human target with body armor) is going to be powerful enough that it'll be ionizing the air to some degree. It'll be like a lightning bolt, there'll be flashes of light and sharp cracking sounds. That's also ignoring the fact that the random bits of terrain that the laser is hitting will also be exploding. Someone under "suppressing fire" from a laser weapon would be quite aware of the fact.
All that said, the successful laser weapons right now seem to all be anti drone/aircraft and they are typically using tracked CW (not pulsed) lasers with heating over time to avoid atmospheric lensing. Lots of challenges to overcome in getting pulsed energy a long way through air.
I was wondering if we'd see pulsed lasers in anti-drone warfare.... the power supply advantages aside, focusing on just the right point in time with the pulse seems hard.
The hard part is predicting atmospheric effects to get the focus right. It's basically impossible without some form of just in time compensation. One idea I've seen is that you fire a physical projectile and use that to calibrate the focal point at arbitrary distance, almost like a laser tracer.
It's not easy but you can correct the atmosphere. This is done with guide stars and adaptive optics.
The bigger challenge is that for intense pulsed lasers, the standard laser profile causes them to self focus in air through nonlinear effects. To overcome this you need to make weird profiles like top hats that are much hard to get just right.
This is a fundamentally physical limitation that is pretty tricky to overcome.
It might be hard, but with the processing power we can fit into microchips these days I'd say we fixed harder problems already. I mean, the controller needs at least two cameras or another methode of locating the target and estimating the distance, but I'd guess we could completely get rid of time of flight calculations as the light pulse would be instant for that matter.